Energy spectra and fluxes for Rayleigh-Benard convection

TL;DR

This study uses high-resolution simulations to analyze energy spectra and fluxes in turbulent Rayleigh-Bénard convection across various Prandtl numbers, supporting Kolmogorov-Obukhov scaling at low Prandtl numbers and suggesting different scaling behaviors at higher Prandtl numbers.

Contribution

It provides detailed spectral and flux analyses for Rayleigh-Bénard convection over a wide range of Prandtl numbers, clarifying the applicability of KO and BO scaling laws in different regimes.

Findings

KO scaling supported at zero and low Prandtl numbers

BO scaling preferred at high Prandtl numbers

Inconclusive results for intermediate and unit Prandtl numbers

Abstract

We compute the spectra and fluxes of the velocity and temperature fields in Rayleigh-B\'{e}nard convection in turbulent regime for a wide range of Prandtl numbers using pseudo-spectral simulations on $512^3$ grids. Our spectral and flux results support the Kolmogorov-Obukhov (KO) scaling for zero Prandtl number and low Prandtl number ($P=0.02$) convection. The KO scaling for the velocity field in zero-Prandtl number and low-Prandtl number convection is because of the weak buoyancy in the inertial range (buoyancy is active only at the very low wavenumbers). We also observe that for intermediate Prandtl numbers ($P=0.2$) the KO scaling fits better with the numerical results than the Bolgiano-Obukhov (BO) scaling. For large Prandtl number ($P=6.8$), the spectra and flux results are somewhat inconclusive on the validity of the KO or BO scaling, yet the BO scaling is preferred over the KO scaling for these cases. The numerical results for P=1 is rather inconclusive.